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Suppose Melissa’s utility over X and Y can be represented by U(X,Y)-Y. Melissa maximizes her utility subject to a budget constraint.

1. Suppose Melissa’s utility over X and Y can be represented by U(X,Y)-Y. Melissa maximizes her utility subject to a budget constraint. What are her uncompensated demand functions, X*(pX, pY, I) and Y*(pX, pY, I)?

X*(pX, pY, I) and Y*(pX, pY, I)/Py

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X*(pX, pY, I)/pX and Y*(pX, pY, I)

X*(pX, pY, I) and Y*(pX, pY, I)/(Py)

X*(pX, pY, I)/pX and Y*(pX, pY, I)

X*(pX, pY, I) and Y*(pX, pY, I)/(2Py)

X*(pX, pY, I)/(2pX) and Y*(pX, pY, I)

2. My utility function U(x,y) only depends on two commodities x and y. When and , my demand functions are such that I spend all of my income on y and never buy any of x, no matter how large or small my income may be. On the basis of this information, my friends have concluded that x is necessarily an economic bad for me. Are they correct?

True

False

3. Suppose you solve a consumer’s problem to maximize her utility subject to her budget constraint — and your answer contains a negative consumption level of good 2! Which of the following is a valid conclusion on your part:

The true optimum has the consumer consume none of good 2.

The true optimum has the consumer consume none of good 1.

There are multiple “true” optimal consumption bundles.

The consumer will sell good 2.

The consumer will sell good 1.

None of the above answers is correct

4. Can a consumer ever be maximizing her utility subject to her budget constraint if the “bang-for-her-buck” (her added utility from the last dollar spent on the good) is not the same across all of the goods she consumes?

Yes

No

5. Matt’s utility over commodities x1 and x2 can be represented by U(x1, x2)(A)+6log(x1)+4log(x2). What is Matt’s ordinary demand function for x1*(p1,p2,I)?

10(I/p1)

.6[I/(p1+p2)]

10I/(p1+p2)

6I/(p1+p2)

0.6(I/p1)

6. Ben gets utility from apples and bananas and his preferences can be represented by the utility function U(A,B)+B. If the price of apples is 3 times the price of bananas, what is Ben’s ordinary demand function for apples, A*(pA, pB, I)?

A*(pA, pB, I)A

A*(pA, pB, I)

A*(pA, pB, I)/(2pA)

A*(pA, pB, I)/(3pA)

A*(pA, pB, I)/pA

 

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